What is 12/40 plus 7/13? (Answer: 109/130)

Exact Answer

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Problem: What is 12/40 plus 7/13?
Formula / Expression: 12/40 + 7/13
Final Answer: 109/130
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.
Working: LCD(40, 13) = 520

Step 2: Convert to Equivalent Fractions with Common Denominator 520
Multiply the numerator and denominator of 12/40 by 13, and multiply the numerator and denominator of 7/13 by 40 so both fractions share the common base 520.
Working: 12 × 13/40 × 13 = 156/520 and 7 × 40/13 × 40 = 280/520

Step 3: Add the Numerators
Now add the numerators (156 + 280 = 436) and keep the common denominator 520 unchanged.
Working: 156 + 280/520 = 436/520

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 436 and 520, which is 4. Divide both the numerator and denominator by 4.
Working: 436 ÷ 4/520 ÷ 4 = 109/130

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 130 produces a repeating decimal (approximately 0.838462, or 83.8462%).
Working: 109 ÷ 130 = 0.838462 (83.8462%)

Key Values:
- Simplified Fraction: 109/130
- Mixed Number Form: 109/130
- Decimal Value: 0.838462
- Percentage: 83.8462%

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Solved with FractionsCalc:
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12/40 + 7/13 = 109/130

Simplified Fraction

109/130

Mixed Number

Proper (109/130)

Decimal Value

0.838462

Percentage

83.8462%

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Step-by-Step Solution: 12/40 + 7/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 13 = 520.

LCD(40, 13) = 520

Step 2

Convert to Equivalent Fractions with Common Denominator 520

Multiply the numerator and denominator of 12/40 by 13, and multiply the numerator and denominator of 7/13 by 40 so both fractions share the common base 520.

12 × 13/40 × 13 = 156/520 and 7 × 40/13 × 40 = 280/520

Step 3

Add the Numerators

Now add the numerators (156 + 280 = 436) and keep the common denominator 520 unchanged.

156 + 280/520 = 436/520

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 436 and 520, which is 4. Divide both the numerator and denominator by 4.

436 ÷ 4/520 ÷ 4 = 109/130

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 130 produces a repeating decimal (approximately 0.838462, or 83.8462%).

109 ÷ 130 = 0.838462 (83.8462%)

Visual Representation

The diagram below illustrates 12/40 plus 7/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/130`
Mixed Number Form	`109/130`
Decimal Form	`0.838462`
Percentage	`83.8462%`

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Frequently Asked Questions

What is 12/40 plus 7/13 as a fraction?

12/40 + 7/13 in simplest fraction form is 109/130.

What is 12/40 plus 7/13 as a decimal?

12/40 + 7/13 converted to a decimal is 0.838462.

What is 12/40 plus 7/13 as a percentage?

12/40 + 7/13 expressed as a percentage is 83.8462%.

Does 12/40 plus 7/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.838462...) because the denominator contains prime factors other than 2 and 5.